Shock wave criterion for propagating solitary states in driven surface waves

Highly localized solitary states are observed to propagate along the surface of a thin two-dimensional fluid layer. The states are driven by means of a spatially uniform, temporally periodic, vertical acceleration (Faraday experiment) in a highly dissipative fluid. These states are shown to be formed by coupled fronts that propagate, periodically, as shock waves. A criterion for their formation based on shock initiation is presented. Both the characteristic form and interaction dynamics of the solitary states can be understood in this picture.